Is your date odd or even?
You're interviewing 100 subjects about their birth dates. For example, if the birth date is April 14, 1994, it will be recorded as 14/4/1994.
There are 52 people who have odd birth date numbers, 54 with odd month numbers, and 60 with odd year numbers. On the other hand, there are 20 people who have even birth date & month numbers, 17 with even month & year numbers, and 15 with even date & year numbers.
If there are 11 people who have all odd day, month, year numbers, how many people have all even day, month, year numbers?
The answer is 7.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let U be the universe set, A = set of even birth date, B = set of even birth month, C = set of even birth year.
|U| = 100. The people with all odd numbers = 11, so the rest is the ones with at least one even number.
|A⋃B⋃C| = 100-11 = 89 = |A|+|B|+|C|-|A⋂B|-|B⋂C|-|A⋂C|+|A⋂B⋂C|
We can calculate |A|,|B|,|C| by subtracting the number of odd date, month, and year people to the total. On the other hand, |A⋂B|,|B⋂C|, & |A⋂C| are already given.
|A⋃B⋃C| = 89 = |A|+|B|+|C|-|A⋂B|-|B⋂C|-|A⋂C|+|A⋂B⋂C|= (100-52)+(100-54)+(100-60) - 20 - 17 - 15 + |A⋂B⋂C|
|A⋂B⋂C|= 89 - 48 - 46 - 40 + 20 + 17 +15 = 7.
Therefore, there are 7 people who have all even date, month, & year numbers.